But for this particular image, I need to specify the min and max values like I have done while using Map.addlayer (for viewing the image) by using nighttimeVis vector. How can I specify the same max and min before or in my Export command for this image?

Do you want to mask all values below and above those values? Or do you want to scale your image such that all values above 60 will be set to 60, and all values below 0 will be set to 0?
– KuikFeb 12 at 11:04

By adding toByte(), you image is stored as a 8-bit integer which would save you some storage space, but you could remove that to keep floating values. Note that now values above 60 are all saved as 255 values. But I think that is what you want.